Formally, the "conn" of a Colonial Fleet warship is the collective name for its helm controls: yaw, pitch, and roll.
The term is also used to grant command of a ship from a commanding officer to a subordinate, typically an Executive officer.
After placing Pegasus is a precarious situation that required his engineering leadership to save the ship, Commander Barry Garner tells Major Lee Adama, "You have the conn" (The Captain's Hand).